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Abstract

We introduce the generalized vector Helmholtz-Gauss (gVHzG) beams that constitute a general family of localized beam solutions of the Maxwell equations in the paraxial domain. The propagation of the electromagnetic components through axisymmetric ABCD optical systems is expressed elegantly in a coordinate-free and closed-form expression that is fully characterized by the transformation of two independent complex beam parameters. The transverse mathematical structure of the gVHzG beams is form-invariant under paraxial transformations. Any paraxial beam with the same waist size and transverse spatial frequency can be expressed as a superposition of gVHzG beams with the appropriate weight factors. This formalism can be straightforwardly applied to propagate vector Bessel-Gauss, Mathieu-Gauss, and Parabolic-Gauss beams, among others.

Propagation of the transverse intensity distribution and electric vector field for generalized vector Bessel-cosine-Gauss, Mathieu-Gauss, and parabolic-Gauss beams. The parameter data for the propagations are included within the text. The movies show the evolution from z=0 to z=4LF
. (Movie files: 3.1 MB, 2.5 MB, 3.6 MB, and 2.2 MB)

Propagation of the transverse intensity distribution and the electric vector field for circularly polarized gVHzG beams constructed with finite superposition of vector Gaussian beams. The parameter data for the propagations are included within the text. The movies show the evolution from z=0 to z=4LF
. (Movie files: 2.4 MB, 2.3 MB, 3.3 MB, and 3.3 MB)